The MUSE Measurement of the Proton Radius at PSI $\pi$M1: Radiative Corrections and Two-Photon Exchange

The MUon proton Scattering Experiment (MUSE) at the Paul Scherrer Institut (PSI) $\pi$M1 beam line is intended to measure the proton charge radius from $\mu^\pm p$ and $e^\pm p$ elastic scattering. In this talk we present calculations and discuss the role of electromagnetic radiative corrections for the MUSE experiment. Since the muon is heavier than an electron, the bremsstrahlung corrections are reduced in the muon case. However, the two-photon corrections and the interference between lepton and proton bremsstrahlung are less dependent on the lepton mass. Model estimates of the two-photon corrections are presented. The MUSE experiment will provide a capability to measure two-photon effects by analyzing lepton charge dependence of the scattering cross sections.